As one of the few people who actually liked and appreciated RE6, I didn't get the feeling that the series had lost its identity until recently. While I do acknowledge the changes that have been made over time, and I certainly don't like every entry in the series equally, it all made sense to me up to and including RE6. In the
poll I made a year ago asking what you think makes RE what it is, most of you agreed with me that the story and characters are most important (not necessarily to enjoy a game per se, but to recognise a new episode as part of an already existing series), and if you look at it from a story perspective, that's just what we had: Zero and RE1/REmake laid the groundwork, RE2 and 3 logically expanded on that by infecting an entire city with the T-virus rather than just one remote location, and Code Veronica showed for the first time that Umbrella is more than just one or two facilities in Raccoon City.
RE4 and 5 added new elements to the story without betraying its roots. Yes, a mind-controlling parasite was now the source of all the chaos rather than a virus turning people into mindless zombies, but the result was pretty much the same: You had to fight your way through hordes of infected who were once ordinary people, and you did that with those same characters introduced in the first games, who had since moved on to work for different organisations, but with the same goal as back then – stopping bioterrorism. I admit they kind of messed up Wesker in RE5, but got many other things right: Leon's new job is a direct consequence of the ending of RE2, Jill's T-virus infection from RE3 comes into play in a meaningful way, Ada is still collecting virus samples for Odin knows who, and a game focusing more on the origins of the BSAA (whose creation also made sense in the game's lore) was given later in the form of Revelations 1.
All of that culminates in RE6: Terror is going global by means of the new C-virus, which is basically a combination of all other viruses previously introduced, several characters from past games return, including Chris and Leon who have never starred in the same game before, and all their stories are intertwined. Sure, there's a whole list of things that could have been done better, some campaigns are clearly more fleshed out than others, and Capcom may have overestimated themselves trying to create a game that pleases everyone (and ended up pleasing no one 100%), but it still felt like a logical continuation of what the series had become up until that point.
Then came RE7 and was like: "Screw this, I'll do what I want!" It gave us a completely new story with completely new characters, only loosely based on previous games by means of a few blink-and-you'll-miss-it references, and a recurring character in a minor role who doesn't look, sound, or act anything like his previous incarnations. It also dramatically lowered the scale from global bioterror to a single person's struggle, which would have been fine if this was a reboot or a spin-off, but no, RE7 still acts like a continuation set in the same universe as the previous games, and fans fall for it because the main location slightly resembles the original mansion and manual saving is back… Yaaay. This is the point where I say the series has lost its way, because there is no red thread anymore, and like the OP said, RE7 didn't even lay out a new one for the next game to pick up. All of this gets even more frustrating when you think about how easily the mess could have been avoided or at least made less terrible by replacing Ethan, Mia, the Bakers and Eveline with Chris, Jill (or Piers), the Burtons and Natalex, but alas... It is what it is now.